Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Biomass. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset

  • The data set has 115221 observations, comprised of 58079 plots.
  • The frequency of growth measurements among plots is as follows (n=1 through 5): 25558, 13784, 12967, 5656, 114.
  • Thus 55.99% of plots have at least two growth measurements.

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4795     4394.3                                
## 2   4794     4208.3  1 185.97  211.86 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18612.85
## 2     2 18407.37
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.12796    0.16873   0.758    0.448    
## alpha  0.63217    0.04075  15.514   <2e-16 ***
## A      3.59033    0.12724  28.216   <2e-16 ***
## k      7.38833    0.78431   9.420   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9369 on 4794 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.092e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 18407.37
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.12796    0.16873   0.758    0.448    
## alpha  0.63217    0.04075  15.514   <2e-16 ***
## A      3.59033    0.12724  28.216   <2e-16 ***
## k      7.38833    0.78431   9.420   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9369 on 4794 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.092e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92687, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.4996, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 21 rows containing missing values (`geom_point()`).
## Warning: Removed 1050 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9777     9697.8                                
## 2   9776     9072.0  1  625.8  674.36 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35844.15
## 2     2 35193.76
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.26421    0.21330   5.927 3.19e-09 ***
## alpha  0.81079    0.02855  28.402  < 2e-16 ***
## A      2.53536    0.09182  27.611  < 2e-16 ***
## k     10.23482    0.59728  17.136  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9633 on 9776 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.167e-06
##   (3196 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 35193.76
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.26421    0.21330   5.927 3.19e-09 ***
## alpha  0.81079    0.02855  28.402  < 2e-16 ***
## A      2.53536    0.09182  27.611  < 2e-16 ***
## k     10.23482    0.59728  17.136  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9633 on 9776 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.167e-06
##   (3196 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 1578 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5424     7458.3                                
## 2   5423     7181.4  1  276.9   209.1 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24022.47
## 2     2 23819.15
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.74246    0.13710  -5.416 6.37e-08 ***
## alpha  0.71420    0.04645  15.376  < 2e-16 ***
## A      5.15045    0.18927  27.212  < 2e-16 ***
## k     15.74832    1.96440   8.017 1.32e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.151 on 5423 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.78e-06
##   (35 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 23819.15
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.74246    0.13710  -5.416 6.37e-08 ***
## alpha  0.71420    0.04645  15.376  < 2e-16 ***
## A      5.15045    0.18927  27.212  < 2e-16 ***
## k     15.74832    1.96440   8.017 1.32e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.151 on 5423 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.78e-06
##   (35 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 16 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2742     3071.9                                
## 2   2741     2862.1  1 209.82  200.94 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 11096.73
## 2     2 10904.53
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.13761    0.27169   0.506    0.613    
## alpha  0.84729    0.05419  15.635   <2e-16 ***
## A      4.27341    0.25025  17.077   <2e-16 ***
## k     20.20001    2.07777   9.722   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.022 on 2741 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.502e-06
##   (809 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 10904.53
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.13761    0.27169   0.506    0.613    
## alpha  0.84729    0.05419  15.635   <2e-16 ***
## A      4.27341    0.25025  17.077   <2e-16 ***
## k     20.20001    2.07777   9.722   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.022 on 2741 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.502e-06
##   (809 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90201, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.6265, p-value = 1.839e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 422 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5267     6923.8                                
## 2   5266     6738.2  1 185.68  145.11 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 22279.18
## 2     2 22137.93
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.05530    0.11325  -9.318   <2e-16 ***
## alpha  0.65905    0.05127  12.855   <2e-16 ***
## A      5.75637    0.22973  25.057   <2e-16 ***
## k     35.12926    3.60650   9.741   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.131 on 5266 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.487e-06
##   (1120 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 22137.93
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.05530    0.11325  -9.318   <2e-16 ***
## alpha  0.65905    0.05127  12.855   <2e-16 ***
## A      5.75637    0.22973  25.057   <2e-16 ***
## k     35.12926    3.60650   9.741   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.131 on 5266 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.487e-06
##   (1120 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 558 rows containing missing values (`geom_point()`).
## Warning: Removed 1002 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8057      19562                                
## 2   8056      17896  1 1665.9  749.93 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42193.22
## 2     2 41477.82
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.84976    0.17604   4.827 1.41e-06 ***
## alpha  0.87179    0.02897  30.091  < 2e-16 ***
## A      4.53035    0.14034  32.281  < 2e-16 ***
## k      1.77001    0.27791   6.369 2.01e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.49 on 8056 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.422e-06
##   (140 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 41477.82
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.84976    0.17604   4.827 1.41e-06 ***
## alpha  0.87179    0.02897  30.091  < 2e-16 ***
## A      4.53035    0.14034  32.281  < 2e-16 ***
## k      1.77001    0.27791   6.369 2.01e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.49 on 8056 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.422e-06
##   (140 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 72 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8011      21190                                
## 2   8010      19445  1 1745.4  719.01 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 41553.79
## 2     2 40866.90
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.69287    0.18809   3.684 0.000231 ***
## alpha  0.87132    0.02918  29.863  < 2e-16 ***
## A      4.59318    0.16365  28.068  < 2e-16 ***
## k      7.19093    0.65146  11.038  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.558 on 8010 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.236e-06
##   (180 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
##   model     AIC
## 1     2 40866.9
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.69287    0.18809   3.684 0.000231 ***
## alpha  0.87132    0.02918  29.863  < 2e-16 ***
## A      4.59318    0.16365  28.068  < 2e-16 ***
## k      7.19093    0.65146  11.038  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.558 on 8010 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.236e-06
##   (180 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 87 rows containing missing values (`geom_point()`).
## Warning: Removed 931 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    830     2260.6                                
## 2    829     2131.2  1 129.37  50.321 2.801e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4393.881
## 2     2 4346.793
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8587     0.8208   1.046    0.296    
## alpha   0.8321     0.1053   7.902 8.70e-15 ***
## A       4.0748     0.6206   6.566 9.11e-11 ***
## k       1.5596     1.1821   1.319    0.187    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.603 on 829 degrees of freedom
## 
## Number of iterations to convergence: 23 
## Achieved convergence tolerance: 8.221e-06
##   (29 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 4346.793
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8587     0.8208   1.046    0.296    
## alpha   0.8321     0.1053   7.902 8.70e-15 ***
## A       4.0748     0.6206   6.566 9.11e-11 ***
## k       1.5596     1.1821   1.319    0.187    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.603 on 829 degrees of freedom
## 
## Number of iterations to convergence: 23 
## Achieved convergence tolerance: 8.221e-06
##   (29 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91018, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.0259, p-value = 0.002479
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (`geom_point()`).
## Warning: Removed 645 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    979     1429.8                              
## 2    978     1418.5  1 11.301  7.7913 0.005352 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4162.017
## 2     2 4156.224
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.02833    0.53460  -0.053  0.95775    
## alpha  0.45520    0.15511   2.935  0.00342 ** 
## A      3.43217    0.41750   8.221 6.39e-16 ***
## k     12.15390    3.79888   3.199  0.00142 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.204 on 978 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 6.251e-06
##   (412 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 4156.224
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.02833    0.53460  -0.053  0.95775    
## alpha  0.45520    0.15511   2.935  0.00342 ** 
## A      3.43217    0.41750   8.221 6.39e-16 ***
## k     12.15390    3.79888   3.199  0.00142 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.204 on 978 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 6.251e-06
##   (412 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.71959, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.9504, p-value = 0.05113
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 220 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    136     120.26                            
## 2    135     117.52  1 2.7361   3.143 0.07851 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 459.1608
## 2     2 457.9617
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     1.5868     2.5256   0.628   0.5309  
## alpha   0.5938     0.3038   1.955   0.0527 .
## A       2.9848     1.3104   2.278   0.0243 *
## k      58.3210    24.2463   2.405   0.0175 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.933 on 135 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.529e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 457.9617
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     1.5868     2.5256   0.628   0.5309  
## alpha   0.5938     0.3038   1.955   0.0527 .
## A       2.9848     1.3104   2.278   0.0243 *
## k      58.3210    24.2463   2.405   0.0175 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.933 on 135 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.529e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90099, p-value = 3.897e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.3818, p-value = 0.167
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1140 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5087     4233.1                                
## 2   5086     3997.3  1 235.83  300.06 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19222.23
## 2     2 18932.46
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8685     0.2251   3.858 0.000116 ***
## alpha   0.6406     0.0345  18.570  < 2e-16 ***
## A       2.9351     0.1209  24.285  < 2e-16 ***
## k       2.8562     0.4807   5.942    3e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8865 on 5086 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.237e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 18932.46
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8685     0.2251   3.858 0.000116 ***
## alpha   0.6406     0.0345  18.570  < 2e-16 ***
## A       2.9351     0.1209  24.285  < 2e-16 ***
## k       2.8562     0.4807   5.942    3e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8865 on 5086 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.237e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 8 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5232      11548                                
## 2   5231      11295  1 252.68  117.02 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25880.58
## 2     2 25766.76
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.09923    0.19061  -0.521    0.603    
## alpha  0.82689    0.07218  11.456  < 2e-16 ***
## A      4.38260    0.19106  22.938  < 2e-16 ***
## k      9.42197    2.10536   4.475 7.79e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.469 on 5231 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.702e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 25766.76
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.09923    0.19061  -0.521    0.603    
## alpha  0.82689    0.07218  11.456  < 2e-16 ***
## A      4.38260    0.19106  22.938  < 2e-16 ***
## k      9.42197    2.10536   4.475 7.79e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.469 on 5231 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.702e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 20 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    598     960.81                                
## 2    597     931.59  1 29.223  18.727 1.768e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2572.128
## 2     2 2555.565
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.0863     1.6829   1.834   0.0672 .  
## alpha   0.9648     0.2063   4.678 3.59e-06 ***
## A       1.8964     0.4344   4.366 1.49e-05 ***
## k       9.2756     6.2080   1.494   0.1357    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.249 on 597 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.796e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 2555.565
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.0863     1.6829   1.834   0.0672 .  
## alpha   0.9648     0.2063   4.678 3.59e-06 ***
## A       1.8964     0.4344   4.366 1.49e-05 ***
## k       9.2756     6.2080   1.494   0.1357    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.249 on 597 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.796e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93069, p-value = 4.695e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.5524, p-value = 0.1206
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    668     936.72                                
## 2    667     894.41  1  42.31  31.552 2.852e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2792.478
## 2     2 2763.464
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     6.6083     3.7929   1.742  0.08192 .  
## alpha   0.9277     0.1535   6.042 2.52e-09 ***
## A       1.2364     0.4243   2.914  0.00369 ** 
## k       3.4720     2.0231   1.716  0.08660 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.158 on 667 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 8.399e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 2763.464
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     6.6083     3.7929   1.742  0.08192 .  
## alpha   0.9277     0.1535   6.042 2.52e-09 ***
## A       1.2364     0.4243   2.914  0.00369 ** 
## k       3.4720     2.0231   1.716  0.08660 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.158 on 667 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 8.399e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95943, p-value = 1.172e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5452, p-value = 0.0003923
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    165     194.45                            
## 2    164     191.09  1 3.3559  2.8801 0.09158 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 584.8960
## 2     2 583.9712
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.4848     2.5848  -0.574    0.566  
## alpha   0.6877     0.3770   1.824    0.070 .
## A      14.5055    15.3585   0.944    0.346  
## k     350.4542   304.9435   1.149    0.252  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.079 on 164 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.983e-06
##   (172 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 583.9712
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.4848     2.5848  -0.574    0.566  
## alpha   0.6877     0.3770   1.824    0.070 .
## A      14.5055    15.3585   0.944    0.346  
## k     350.4542   304.9435   1.149    0.252  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.079 on 164 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.983e-06
##   (172 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96329, p-value = 0.0002053
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.4867, p-value = 0.1371
## alternative hypothesis: two.sided

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 86 rows containing missing values (`geom_point()`).
## Warning: Removed 1274 rows containing missing values (`geom_line()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    217     220.35                                
## 2    216     199.78  1 20.567  22.236 4.324e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 664.8357
## 2     2 645.2795
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2157     1.5963   0.135  0.89262    
## alpha   0.8899     0.1621   5.490 1.12e-07 ***
## A       2.5535     0.9059   2.819  0.00527 ** 
## k      39.5775    14.6677   2.698  0.00752 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9617 on 216 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.903e-06
##   (90 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 645.2795
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2157     1.5963   0.135  0.89262    
## alpha   0.8899     0.1621   5.490 1.12e-07 ***
## A       2.5535     0.9059   2.819  0.00527 ** 
## k      39.5775    14.6677   2.698  0.00752 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9617 on 216 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.903e-06
##   (90 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.72946, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.22674, p-value = 0.8206
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 45 rows containing missing values (`geom_point()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 2
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4834 2417 0.1279608 0.0284711 -0.2028349 0.4587565 0.6321701 0.0016604 0.5522851 0.7120551 3.590326 3.3408714 3.839781 7.388327 5.8507221 8.925931
212 Laurentian Mixed Forest east 12976 6488 1.2642107 0.0454952 0.8461062 1.6823151 0.8107858 0.0008149 0.7548275 0.8667442 2.535356 2.3553622 2.715350 10.234816 9.0640147 11.405618
221 Eastern Broadleaf Forest east 5462 2731 -0.7424615 0.0187962 -1.0112313 -0.4736918 0.7142025 0.0021574 0.6231456 0.8052594 5.150452 4.7794010 5.521503 15.748319 11.8972981 19.599340
222 Midwest Broadleaf Forest east 3554 1777 0.1376068 0.0738143 -0.3951269 0.6703405 0.8472928 0.0029368 0.7410318 0.9535539 4.273414 3.7827200 4.764108 20.200006 16.1258614 24.274150
223 Central Interior Broadleaf Forest east 6390 3195 -1.0553007 0.0128260 -1.2773216 -0.8332798 0.6590475 0.0026282 0.5585451 0.7595500 5.756372 5.3059987 6.206746 35.129260 28.0590337 42.199487
231 Southeastern Mixed Forest east 8200 4100 0.8497628 0.0309895 0.5046821 1.1948436 0.8717944 0.0008394 0.8150015 0.9285873 4.530354 4.2552477 4.805460 1.770008 1.2252304 2.314785
232 Outer Coastal Plain Mixed Forest east 8194 4097 0.6928677 0.0353768 0.3241676 1.0615678 0.8713182 0.0008513 0.8141241 0.9285124 4.593184 4.2723916 4.913976 7.190935 5.9138993 8.467970
234 Lower Mississippi Riverine Forest east 862 431 0.8586775 0.6736916 -0.7523880 2.4697431 0.8321212 0.0110883 0.6254332 1.0388092 4.074795 2.8566903 5.292899 1.559619 -0.7606964 3.879934
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 -0.0283305 0.2858016 -1.0774338 1.0207728 0.4552015 0.0240589 0.1508159 0.7595870 3.432175 2.6128668 4.251482 12.153899 4.6990033 19.608794
255 Prairie Parkland (Subtropical) east 446 223 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 1.5868390 6.3786373 -3.4080136 6.5816916 0.5937701 NA -0.0069897 1.1945298 2.984765 0.3932120 5.576318 58.321034 10.3693915 106.272676
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 0.8685334 0.0506691 0.4272444 1.3098225 0.6406419 0.0011902 0.5730094 0.7082744 2.935133 2.6981928 3.172073 2.856217 1.9139315 3.798502
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 -0.0992304 0.0363308 -0.4728986 0.2744378 0.8268867 0.0052096 0.6853889 0.9683845 4.382597 4.0080362 4.757157 9.421972 5.2945838 13.549361
M223 Ozark Broadleaf Forest Meadow east 604 302 3.0862540 2.8322583 -0.2189318 6.3914398 0.9648155 0.0425404 0.5597454 1.3698855 1.896405 1.0433144 2.749496 9.275595 -2.9165719 21.467762
M231 Ouachita Mixed Forest east 678 339 6.6083045 14.3861669 -0.8391767 14.0557857 0.9277099 0.0235722 0.6262449 1.2291749 1.236440 0.4033305 2.069550 3.471953 -0.5004547 7.444361
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -1.4848044 6.6812476 -6.5886030 3.6189941 0.6876548 0.1421385 -0.0567697 1.4320792 14.505455 -15.8203490 44.831260 350.454245 -251.6671657 952.575656
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 0.2157499 2.5482666 -2.9306267 3.3621265 0.8898888 0.0262753 0.5703953 1.2093823 2.553540 0.7680136 4.339067 39.577528 10.6673265 68.487729
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 20 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 20 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (productivity trend (in %) 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US  0.463104049            0.079886499     0.61968159
## 2       pacific -0.007761654            0.013511819     0.01872151
## 3          east  0.466080247            0.078138581     0.61923187
## 4 interior west  0.004785457            0.009677066     0.02375251
##   95 % CI, lower
## 1     0.30652651
## 2    -0.03424482
## 3     0.31292863
## 4    -0.01418159

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.765261331             0.0135256930    0.791771689
## 2       pacific    0.003594641             0.0019707926    0.007457394
## 3          east    0.756019476             0.0133590222    0.782203159
## 4 interior west    0.005647214             0.0007725766    0.007161465
##   95 % CI, lower
## 1   0.7387509726
## 2  -0.0002681127
## 3   0.7298357923
## 4   0.0041329641

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   3.992012
## 2       pacific  13.047235
## 3          east   3.958788
## 4 interior west   1.961209

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   13.14609
## 2       pacific  315.22340
## 3          east   11.16176
## 4 interior west   33.30795

Analysis 2: Temporally-balanced, No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3724     3417.2                                
## 2   3723     3391.4  1 25.757  28.276 1.114e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14508.81
## 2     2 14482.61
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.03073    0.18885   0.163    0.871    
## alpha  0.53669    0.09686   5.541 3.21e-08 ***
## A      3.59150    0.14566  24.657  < 2e-16 ***
## k      7.26908    0.86336   8.420  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9544 on 3723 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.194e-06
##   (33 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_211,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 14482.61
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.03073    0.18885   0.163    0.871    
## alpha  0.53669    0.09686   5.541 3.21e-08 ***
## A      3.59150    0.14566  24.657  < 2e-16 ***
## k      7.26908    0.86336   8.420  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9544 on 3723 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.194e-06
##   (33 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91849, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.0619, p-value = 7.514e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (`geom_point()`).
## Warning: Removed 1050 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7890     7621.3                                
## 2   7889     7527.4  1 93.969  98.484 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28703.69
## 2     2 28607.77
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.95442    0.21791    4.38  1.2e-05 ***
## alpha  0.60286    0.05787   10.42  < 2e-16 ***
## A      2.66571    0.10561   25.24  < 2e-16 ***
## k     12.61290    0.77788   16.21  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9768 on 7889 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.864e-06
##   (2589 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_212,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 28607.77
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.95442    0.21791    4.38  1.2e-05 ***
## alpha  0.60286    0.05787   10.42  < 2e-16 ***
## A      2.66571    0.10561   25.24  < 2e-16 ***
## k     12.61290    0.77788   16.21  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9768 on 7889 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.864e-06
##   (2589 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 1313 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   4441     6146.1                              
## 2   4440     6085.7  1 60.442  44.097 3.5e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19769.06
## 2     2 19727.14
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.82538    0.14806  -5.575 2.63e-08 ***
## alpha  0.60176    0.08747   6.880 6.83e-12 ***
## A      5.25079    0.21634  24.271  < 2e-16 ***
## k     17.27045    2.28363   7.563 4.77e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.171 on 4440 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.773e-06
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 19727.14
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.82538    0.14806  -5.575 2.63e-08 ***
## alpha  0.60176    0.08747   6.880 6.83e-12 ***
## A      5.25079    0.21634  24.271  < 2e-16 ***
## k     17.27045    2.28363   7.563 4.77e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.171 on 4440 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.773e-06
##   (32 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87959, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.423, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2144     2308.5                                
## 2   2143     2245.5  1  63.03  60.154 1.346e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8572.838
## 2     2 8515.402
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.07442    0.28535  -0.261    0.794    
## alpha  0.76489    0.09167   8.344   <2e-16 ***
## A      4.37310    0.28154  15.533   <2e-16 ***
## k     21.10209    2.35205   8.972   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.024 on 2143 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.475e-06
##   (651 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 8515.402
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.07442    0.28535  -0.261    0.794    
## alpha  0.76489    0.09167   8.344   <2e-16 ***
## A      4.37310    0.28154  15.533   <2e-16 ***
## k     21.10209    2.35205   8.972   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.024 on 2143 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.475e-06
##   (651 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91322, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.2187, p-value = 5.014e-10
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 340 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4276     5695.6                                
## 2   4275     5657.3  1  38.24  28.896 8.043e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18182.73
## 2     2 18155.91
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.14606    0.12313  -9.307  < 2e-16 ***
## alpha  0.54024    0.09692   5.574 2.64e-08 ***
## A      5.71873    0.25314  22.591  < 2e-16 ***
## k     33.51573    3.88016   8.638  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 4275 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 8.25e-06
##   (843 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 18155.91
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.14606    0.12313  -9.307  < 2e-16 ***
## alpha  0.54024    0.09692   5.574 2.64e-08 ***
## A      5.71873    0.25314  22.591  < 2e-16 ***
## k     33.51573    3.88016   8.638  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 4275 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 8.25e-06
##   (843 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 408 rows containing missing values (`geom_point()`).
## Warning: Removed 1002 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6314      14258                                
## 2   6313      14075  1 182.61  81.904 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32889.13
## 2     2 32809.70
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.75145    0.19412   3.871 0.000109 ***
## alpha  0.73004    0.07694   9.489  < 2e-16 ***
## A      4.53651    0.15788  28.733  < 2e-16 ***
## k      2.16383    0.35586   6.081 1.27e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.493 on 6313 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.246e-06
##   (127 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_231,  : 
##   object 'ge.fit' not found
##   model     AIC
## 1     2 32809.7
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.75145    0.19412   3.871 0.000109 ***
## alpha  0.73004    0.07694   9.489  < 2e-16 ***
## A      4.53651    0.15788  28.733  < 2e-16 ***
## k      2.16383    0.35586   6.081 1.27e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.493 on 6313 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.246e-06
##   (127 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 60 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6387      15897                                
## 2   6386      15679  1 217.93  88.761 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33025.57
## 2     2 32939.37
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.54711    0.20463   2.674  0.00752 ** 
## alpha  0.67053    0.06749   9.935  < 2e-16 ***
## A      4.68597    0.18895  24.801  < 2e-16 ***
## k      8.91008    0.84283  10.572  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.567 on 6386 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.527e-06
##   (150 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_232,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 32939.37
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.54711    0.20463   2.674  0.00752 ** 
## alpha  0.67053    0.06749   9.935  < 2e-16 ***
## A      4.68597    0.18895  24.801  < 2e-16 ***
## k      8.91008    0.84283  10.572  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.567 on 6386 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.527e-06
##   (150 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 75 rows containing missing values (`geom_point()`).
## Warning: Removed 931 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    684     1785.1                                
## 2    683     1734.9  1 50.129  19.734 1.038e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3613.269
## 2     2 3595.701
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.25438    0.71374   0.356    0.722    
## alpha  0.81570    0.17001   4.798 1.97e-06 ***
## A      4.38706    0.64951   6.754 3.07e-11 ***
## k      0.08434    0.20431   0.413    0.680    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.594 on 683 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 7.72e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 3595.701
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.25438    0.71374   0.356    0.722    
## alpha  0.81570    0.17001   4.798 1.97e-06 ***
## A      4.38706    0.64951   6.754 3.07e-11 ***
## k      0.08434    0.20431   0.413    0.680    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.594 on 683 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 7.72e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93551, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.6254, p-value = 0.008654
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).
## Warning: Removed 645 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    868     1343.8                            
## 2    867     1338.7  1 5.0919  3.2977 0.06972 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3738.098
## 2     2 3736.791
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.08182    0.57699  -0.142  0.88727    
## alpha  0.39484    0.20828   1.896  0.05832 .  
## A      3.38977    0.44598   7.601 7.64e-14 ***
## k     11.46044    3.96871   2.888  0.00398 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.243 on 867 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.542e-06
##   (349 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 3736.791
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.08182    0.57699  -0.142  0.88727    
## alpha  0.39484    0.20828   1.896  0.05832 .  
## A      3.38977    0.44598   7.601 7.64e-14 ***
## k     11.46044    3.96871   2.888  0.00398 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.243 on 867 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.542e-06
##   (349 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.71043, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.4474, p-value = 0.0005661
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 159 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    128    101.432                            
## 2    127     98.965  1 2.4665  3.1652 0.07762 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 420.8587
## 2     2 419.6338
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.8695     1.9102   0.455   0.6497  
## alpha   0.5777     0.2932   1.970   0.0510 .
## A       3.4946     1.3377   2.612   0.0101 *
## k      58.0814    22.5453   2.576   0.0111 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8828 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.549e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_332,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 419.6338
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.8695     1.9102   0.455   0.6497  
## alpha   0.5777     0.2932   1.970   0.0510 .
## A       3.4946     1.3377   2.612   0.0101 *
## k      58.0814    22.5453   2.576   0.0111 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8828 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.549e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89705, p-value = 4.933e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1251, p-value = 0.2605
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1140 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3950     3001.9                                
## 2   3949     2983.3  1 18.581  24.596 7.366e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14658.10
## 2     2 14635.55
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.94921    0.26165   3.628  0.00029 ***
## alpha  0.45788    0.08907   5.140 2.87e-07 ***
## A      2.81257    0.13373  21.032  < 2e-16 ***
## k      2.40480    0.47337   5.080 3.95e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8692 on 3949 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.432e-06
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M211,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 14635.55
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.94921    0.26165   3.628  0.00029 ***
## alpha  0.45788    0.08907   5.140 2.87e-07 ***
## A      2.81257    0.13373  21.032  < 2e-16 ***
## k      2.40480    0.47337   5.080 3.95e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8692 on 3949 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.432e-06
##   (13 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9814, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.6036, p-value = 2.879e-14
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4659      10327                                
## 2   4658      10238  1 89.796  40.857 1.798e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23096.71
## 2     2 23057.99
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1667     0.1983  -0.841    0.401    
## alpha   0.8093     0.1215   6.663 2.99e-11 ***
## A       4.4088     0.2043  21.579  < 2e-16 ***
## k       9.8033     2.2913   4.279 1.92e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.483 on 4658 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.654e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M221,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 23057.99
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1667     0.1983  -0.841    0.401    
## alpha   0.8093     0.1215   6.663 2.99e-11 ***
## A       4.4088     0.2043  21.579  < 2e-16 ***
## k       9.8033     2.2913   4.279 1.92e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.483 on 4658 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.654e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86979, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.5674, p-value = 5.122e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    524     819.79                            
## 2    523     814.78  1 5.0148   3.219 0.07337 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2249.276
## 2     2 2248.042
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.6120     1.5870   1.646   0.1004    
## alpha   0.7193     0.3836   1.875   0.0613 .  
## A       2.1379     0.5145   4.156 3.79e-05 ***
## k      18.4775    10.2802   1.797   0.0729 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.248 on 523 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.752e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 2248.042
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.6120     1.5870   1.646   0.1004    
## alpha   0.7193     0.3836   1.875   0.0613 .  
## A       2.1379     0.5145   4.156 3.79e-05 ***
## k      18.4775    10.2802   1.797   0.0729 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.248 on 523 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.752e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9264, p-value = 2.132e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.3291, p-value = 0.1838
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (`geom_point()`).
## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    581     732.19                              
## 2    580     722.39  1 9.7989  7.8674 0.005202 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2364.027
## 2     2 2358.158
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     5.5161     3.1963   1.726  0.08492 . 
## alpha   1.0485     0.3536   2.965  0.00315 **
## A       1.6402     0.5390   3.043  0.00245 **
## k      21.4176     7.0809   3.025  0.00260 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.116 on 580 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 7.903e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M231,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 2358.158
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     5.5161     3.1963   1.726  0.08492 . 
## alpha   1.0485     0.3536   2.965  0.00315 **
## A       1.6402     0.5390   3.043  0.00245 **
## k      21.4176     7.0809   3.025  0.00260 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.116 on 580 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 7.903e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97305, p-value = 6.907e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.8918, p-value = 0.00383
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    156     186.49                            
## 2    155     182.34  1 4.1465  3.5247 0.06234 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 555.0482
## 2     2 553.4730
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.7886     2.1337  -0.838   0.4032  
## alpha   0.7789     0.3841   2.028   0.0443 *
## A      13.3571    12.6238   1.058   0.2917  
## k     270.2899   210.0776   1.287   0.2001  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.085 on 155 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.586e-06
##   (163 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M261,  : 
##   object 'ge.fit' not found
##   model     AIC
## 1     2 553.473
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.7886     2.1337  -0.838   0.4032  
## alpha   0.7789     0.3841   2.028   0.0443 *
## A      13.3571    12.6238   1.058   0.2917  
## k     270.2899   210.0776   1.287   0.2001  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.085 on 155 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.586e-06
##   (163 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96531, p-value = 0.0005074
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.5145, p-value = 0.1299
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 83 rows containing missing values (`geom_point()`).
## Warning: Removed 1274 rows containing missing values (`geom_line()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    180     187.48                              
## 2    179     177.39  1 10.092  10.184 0.001673 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 561.9578
## 2     2 553.8317
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8928     2.3638   0.378  0.70609    
## alpha   0.8966     0.2556   3.508  0.00057 ***
## A       2.2580     1.0249   2.203  0.02885 *  
## k      41.5917    17.1706   2.422  0.01642 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9955 on 179 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.03e-06
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M334,  : 
##   object 'ge.fit' not found
##   model      AIC
## 1     2 553.8317
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8928     2.3638   0.378  0.70609    
## alpha   0.8966     0.2556   3.508  0.00057 ***
## A       2.2580     1.0249   2.203  0.02885 *  
## k      41.5917    17.1706   2.422  0.01642 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9955 on 179 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.03e-06
##   (75 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.72277, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.48726, p-value = 0.6261
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 35 rows containing missing values (`geom_point()`).
## Warning: Removed 1 rows containing missing values (`geom_segment()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

## Warning: Removed 1 rows containing missing values (`geom_segment()`).

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 2
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4834 2417 0.0307348 0.0356626 -0.3395158 0.4009854 0.5366872 0.0093811 0.3467912 0.7265832 3.591496 3.3059187 3.877073 7.2690758 5.5763777 8.9617738
212 Laurentian Mixed Forest east 12976 6488 0.9544216 0.0474836 0.5272655 1.3815778 0.6028578 0.0033489 0.4894187 0.7162968 2.665713 2.4586869 2.872739 12.6128998 11.0880403 14.1377594
221 Eastern Broadleaf Forest east 5462 2731 -0.8253826 0.0219215 -1.1156522 -0.5351130 0.6017614 0.0076507 0.4302801 0.7732428 5.250788 4.8266466 5.674929 17.2704506 12.7934007 21.7475005
222 Midwest Broadleaf Forest east 3554 1777 -0.0744190 0.0814267 -0.6340178 0.4851798 0.7648889 0.0084042 0.5851089 0.9446689 4.373100 3.8209878 4.925213 21.1020876 16.4895458 25.7146294
223 Central Interior Broadleaf Forest east 6390 3195 -1.1460557 0.0151617 -1.3874596 -0.9046517 0.5402401 0.0093929 0.3502321 0.7302480 5.718731 5.2224514 6.215011 33.5157251 25.9086070 41.1228432
231 Southeastern Mixed Forest east 8200 4100 0.7514525 0.0376820 0.3709141 1.1319910 0.7300422 0.0059191 0.5792227 0.8808616 4.536512 4.2270053 4.846018 2.1638330 1.4662259 2.8614400
232 Outer Coastal Plain Mixed Forest east 8194 4097 0.5471111 0.0418722 0.1459734 0.9482488 0.6705347 0.0045549 0.5382322 0.8028372 4.685965 4.3155689 5.056362 8.9100761 7.2578408 10.5623113
234 Lower Mississippi Riverine Forest east 862 431 0.2543828 0.5094240 -1.1470042 1.6557698 0.8156986 0.0289048 0.4818855 1.1495117 4.387056 3.1117811 5.662330 0.0843379 -0.3168208 0.4854966
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 -0.0818190 0.3329193 -1.2142826 1.0506445 0.3948426 NA -0.0139415 0.8036267 3.389765 2.5144444 4.265086 11.4604392 3.6710413 19.2498372
255 Prairie Parkland (Subtropical) east 446 223 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 0.8695397 3.6488425 -2.9103902 4.6494696 0.5777227 NA -0.0024404 1.1578859 3.494613 0.8476030 6.141623 58.0814043 13.4683245 102.6944841
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 0.9492095 0.0684631 0.4362188 1.4622003 0.4578758 0.0079339 0.2832433 0.6325083 2.812567 2.5503888 3.074746 2.4047995 1.4767252 3.3328738
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 -0.1667323 0.0393256 -0.5555075 0.2220430 0.8093399 0.0147544 0.5712057 1.0474742 4.408786 4.0082448 4.809327 9.8032695 5.3112649 14.2952740
M223 Ozark Broadleaf Forest Meadow east 604 302 2.6120500 2.5186583 -0.5056830 5.7297829 0.7193302 NA -0.0342572 1.4729176 2.137883 1.1272249 3.148541 18.4775170 -1.7180528 38.6730867
M231 Ouachita Mixed Forest east 678 339 5.5161264 10.2166025 -0.7616891 11.7939420 1.0484776 0.1250285 0.3539974 1.7429579 1.640184 0.5814777 2.698890 21.4175745 7.5103402 35.3248087
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -1.7886265 4.5525652 -6.0034589 2.4262058 0.7788800 0.1475292 0.0201432 1.5376168 13.357096 -11.5797974 38.293990 270.2898590 -144.6946651 685.2743832
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 0.8928341 5.5874617 -3.7716283 5.5572964 0.8966265 0.0653123 0.3923231 1.4009300 2.258047 0.2356876 4.280407 41.5916937 7.7088672 75.4745202
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 20 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 20 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US  0.311719729             0.08009314     0.46870229
## 2       pacific -0.009349851             0.01115355     0.01251111
## 3          east  0.314755388             0.07837811     0.46837649
## 4 interior west  0.006314192             0.01214007     0.03010873
##   95 % CI, lower
## 1     0.15473717
## 2    -0.03121081
## 3     0.16113429
## 4    -0.01748035

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.630077177              0.026282736    0.681591340
## 2       pacific    0.004071511              0.002007816    0.008006831
## 3          east    0.620364334              0.026177609    0.671672449
## 4 interior west    0.005641332              0.001218051    0.008028712
##   95 % CI, lower
## 1    0.578563015
## 2    0.000136191
## 3    0.569056220
## 4    0.003253953

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   4.036723
## 2       pacific  12.014319
## 3          east   4.010511
## 4 interior west   1.940697

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   13.71999
## 2       pacific  243.11786
## 3          east   12.16129
## 4 interior west   34.22878